1. Field of the Invention
The present invention relates to a capillary rheometer for establishing compressibility material properties and pertains, more particularly to a capillary rheometer which utilizes a pressure measurement plunger for such purposes.
2. Background
Various types of capillary rheometers are utilized in the polymer industry to establish shear and temperature related material properties as well as compressibility properties. The theory of operation and design specifications for capillary rheometers are documented in U.S. Pat. No. 3,203,225.
Capillary rheometers generally operate by using a piston or plunger to force melted polymers, that have been heated in a barrel passage, through a capillary die. The force based plunger-barrel capillary rheometer utilizes a force sensor to measure the load or force applied to the plunger and a displacement sensor to measure the plunger velocity (displacement/unit time) through the stationary barrel. The apparent shear viscosity of the melted polymer can be determined using known relationships for flow of polymer melts through the cylindrical or other commonly used geometries. For example, wide thin slits or annulus geometries may be used. The apparent shear viscosity of a polymer melt at a given melt temperature is determined using the ratio of wall shear stress divided by apparent wall shear rate, for the capillary of a defined geometry. The wall shear stress depends upon the plunger force measured by the force sensor.
In addition to establishing shear and temperature related material properties, capillary rheometers can be modified to generate information on the compressibility of polymer melts. In such an application, the pressure-volume-temperature (PVT) relationships, so called "equation of state" relationships, of a polymer melt can be determined using the capillary rheometer in the following manner. The rheometer barrel is heated to a desired temperature in which polymer granules, pellets or powder are loaded into the barrel and allowed to soften due to the heat. A plunger is used to apply various levels of pressure to the polymer via weights, air pressure, mechanical pressure, or hydraulic pressure. A known diameter plunger with a force measuring sensor is used to determine the pressure within the polymer melt. The temperature of the polymer melt, and the volume of the polymer melt are determined as a function of applied pressure. The specific volume of the polymer, at various pressures, is plotted against polymer temperature to describe the PVT behavior of the polymer.
There are, however, a number of errors associated with the melted polymer apparent viscosity data and compressibility data determined using the above mentioned method. With respect to viscosity measurements, the shear stress and the apparent shear rate values have errors associated therewith. These errors will be described, in particular, with reference to a prior art embodiment of the present invention, as illustrated in FIGS. 1 and 2.
Shear stress values will be in error if determined by means of a force sensor, because the force at the top of the plunger is influenced by the following factors which are not considered when the force sensor method is employed:
1. The Pressure Drop in the Barrel: The barrel 6 of the capillary rheometer is itself a capillary of given diameter and continuously decreasing effective length as the plunger 5 moves downward. The force required to maintain flow through the barrel 6 (i.e., pressure drop along barrel 6) can be significant, especially since the shear rate associated with barrel flow is low, and melted polymers have relatively high viscosities at low shear rates as most polymers are pseudoplastic in nature. The pressure drop is not considered by the force sensor measurement and thus a resulting error occurs in capillary wall shear stress since the stress value calculated assumes all of the pressure drop is due to the capillary itself. In addition, this error is not a "constant" at a given temperature and plunger 5 speed since the effective length of the barrel 6 changes continuously.
2. Friction Between Plunger and Reservoir Wall: In order to minimize the flow of material back across the land of the plunger 5, the plunger 5 must be fitted tightly within the barrel 6. The plunger 5 may be relieved some distance back from the melted polymer 9 interface, although enough tightly fitted land must remain to (i) limit the back flow of melted polymer 9 and (ii) align the tip of the plunger 5 in the barrel 6. Low coefficient of friction plunger seals 8 are often used to reduce the back flow of the melted polymer 9.
The melted polymer 9 may stick to the wall of the barrel and may be sheared between the wall and the plunger 5 as the plunger 5 moves. The plunger 5 itself will rub against the barrel 6 wall unless it is perfectly straight, properly aligned, and has the correct dimensions. High pressures in the barrel 6, such as those encountered when working with viscous materials at high flow rates, could cause buckling of the plunger 5 within the barrel 6, and binding between the plunger 5 and barrel 6. The dimensions of both the plunger 5 tip and barrel 6 will also change when the operating temperature is changed. Changes in operating temperatures could result in scoring of the barrel 6, or the opening (or closing) of the gap through which back flow can occur due to thermal expansion differences between the plunger and the barrel. Therefore, plunger friction errors are likely to occur.
Plunger 5 friction errors are typically estimated by removing the capillary 12 and measuring the force required to force melted polymer 9 from the barrel 6, and extrapolating this to force data to a zero barrel length. The method has been criticized since the friction errors vary with driving pressure and flow rate, and it is also time consuming.
3. End Errors: The entrance area of capillary 12 and barrel 6 exit area is a region where large stresses are developed due to the funneling of the melted polymer 9 as it emerges from the barrel reservoir, as well as region where these stresses relax to their limiting value which occurs some distance along the length of the capillary 12 tube.
The exit pressure for capillary 12 has also been shown to be somewhat greater than zero for viscoelastic polymers. The exit pressure is the result of recoverable elastic energy within the melted polymer 9, caused by flow induced orientation of the polymer molecules during deformation upstream of the capillary 12 exit. Purely viscous materials have exit pressures of zero.
The end errors can be minimized using dies having longer L/D ratios, since they are essentially constants at a given temperature and rate, being independent of capillary 12 length. It should be appreciated that the end errors are a constant and, therefore, become smaller on a percentage basis as the capillary length increases. The errors can be eliminated using the procedure of classical hydrodynamics of plotting the pressure drop measured over a system containing both an entrance region and straight capillary 12 versus the L/R of the tube, for tubes of various lengths and constant diameter at each flow (or shear) rate. Extrapolation to a pressure drop at zero length gives the end effect in terms of absolute pressure. Extrapolation to zero pressure gives the end effect in terms of tube radii. An alternative method is to use a flow geometry, such as a wide thin slit, for which the pressure drop within the rheometric region of the flow can be measured directly.
4. Temperature and Compressibility: It is generally assumed that the temperature of the melted polymer 9 is constant, and that the melted polymer 9 is incompressible. Melted polymers 9 are in fact, however, compressible, and are generally viscous materials, having relatively low thermal diffusitivities, indicating that the temperature of the polymer is likely to increase as it progresses through the measurement system due to viscous dissipation, to a degree depending on conductive heat loss. In order to minimize viscous heating and compressibility effects, short L/D capillaries 12 are recommended, provided end errors and barrel 6 related errors can be accounted for, since their relative effect is more significant for shorter capillaries 12.
5. Elastic Distortion: Elastic distortion of the barrel and polymer viscosity both change with temperature and pressure, plunger velocity, alignment and force. These changes as well as seal quality affect the calculation of effective area used to determine the pressure generated within the barrel of the capillary rheometer. The exact magnitude of these errors in a capillary rheometer are unknown although elastic distortion and effective area calculations are well documented for dead weight piston gages.
The force/sensor pressure calculation does not take into consideration the clearance area between the plunger 5 and the inner barrel wall. The elastic distortion of the barrel and polymer viscosity change with temperature and pressure and plunger velocity. These unaccounted for changes cause errors in effective area and other related calculations.
6. Polymer Backflow/Leakage/Shear Rate Errors: The rate at which melted polymer 9 flows through the capillary 12 is assumed to be equivalent to the value determined using the distance swept by the plunger 5 per unit time, assuming incompressibility and mass conservation. There will however be some leakage of material across the land of the plunger 5, since the pressure on the melted polymer 9 is greater than atmospheric. The amount of back flow will be determined by the quality of the plunger seal 8. Close, tight tolerances between the barrel 6 and plunger 5 will reduce leakage. An increase in the land length (contact area) will also reduce leakage. However, an increase in the number of plunger seals 8, or in the contact area between the plunger 5 and barrel 6, is also expected to increase the magnitude of the plunger 5 barrel 6 friction force errors.
Force sensor pressure calculations do not take into consideration some leakage of the melted polymer across the plunger. There is, however, some leakage of the melted polymer across the plunger. Thus, errors are associated with this calculation. By increasing the number of plunger seals or the contact area between the plunger and inner barrel wall, while it reduces the leakage, it increases the friction errors.
Accordingly, it is an object of the present invention to provide an improved capillary rheometer which eliminates the need for a force based measurement plunger.
It is another object of the present invention to provide a capillary rheometer in which accurate shear stress and apparent shear rate values for a melted polymer can be determined.
It is another object of the present invention to provide a capillary rheometer in which accurate compressibility data for a melted polymer can be determined.
It is another object of the present invention to provide a capillary rheometer which will eliminate the need for corrective methods to account for errors due to the barrel pressure drop, friction between the plunger and inner barrel wall, end errors, temperature and compressibility errors, elastic distortion errors, leakage errors and other related errors.
It is another object of the present invention to provide a capillary rheometer which utilizes a pressure measurement plunger.
It is another object of the present invention to provide a capillary rheometer which utilizes a pressure sensor for sensing pressure exerted by the melted polymer.